TwoSampleAalenJohansen function

Risk difference and ratio using the Aalen-Johansen method

Computes an (absolute) risk difference or ratio with right-censored competing risks data, together with a confidence interval and a p-value (to test for a difference between the two risks). Pointwise estimates are computed via the Aalen-Johansen estimator. Computation of confidence intervals and p-values are based on either Empirical Likelihood (EL) inference or Wald-type inference. Both are non-parametric approaches, which are asymptotically equivalent. For the Wald-type approach, the asymptotic normal approximation is used on the log scale for the risk ratio. No transformation is used for the risk difference. See Blanche & Eriksson (2023) for details.

TwoSampleAalenJohansen(
  time,
  cause,
  group,
  t,
  RR.H0 = 1,
  Diff.H0 = 0,
  level = 0.95,
  contr = list(tol = 1e-05, algo = 2, k = 3, Trace = FALSE, method = "both")
)

Arguments

• time: vector of times (possibly censored)
• cause: vector of event types/causes. It should be coded 1 for main events, 2 for competing events and 0 for censored.
• group: vector of binary group indicator. The reference group should be coded 0, the other 1.
• t: the time point of interest (e.g. 1 to compute a 1-year risk ratio)
• RR.H0: the risk ratio under the null hypothesis, to compute a p-value. Default is 1.
• Diff.H0: the risk difference under the null hypothesis, to compute a p-value. Default is 0.
• level: confidence level for the confidence intervals. Default is 0.95.
• contr: list of control parameters. tol=tolerance for numerical computation, default is 1e-5. method="EL", "Wald" or "both" indicates wether 95% CI and the p-value should be computed based on Empirical Likelihood (EL) inference, Wald-type inference or both. algo=2 (default) or 1, depending on which computational method should be used to maximize the empirical likelihood (method 1 or 2, as described in Blanche & Eriksson (2023))

Returns

an object of class 'TwoSampleAalenJohansen'

Examples

## A simple example for Wald-type inference, using simulated data.
## It illustrates the possible inconsistency of Wald-type inference, in
## terms of statistical significance, when inference is based on the risk
## ratio and on the risk difference. This inconsistency cannot exist
## using an empirical likelihood approach.

ResSimA100 <- TwoSampleAalenJohansen(time=SimA100$time,
                                     cause=SimA100$status,
                                     group=SimA100$group,
                                     t=1,
                                     contr=list(method="Wald"))
ResSimA100

## Same example data, but now analyzed with and empirical likelihood approach. It
## takes approx 20 seconds to run.

ResSimA100 <- TwoSampleAalenJohansen(time=SimA100$time,
                                     cause=SimA100$status,
                                     group=SimA100$group,
                                     t=1)
ResSimA100

References

Blanche & Eriksson (2023). Empirical likelihood comparison of absolute risks.

Author(s)

Paul Blanche